After Cheap Trick ended the regular portion of the Rock and Roll Hall of Fame induction ceremony with a fiery performance, the band stayed onstage to lend its firepower to the final jam session, which drew inductees, speech-givers and tribute performers alike back to the stage.

The group selection ended up being a cover of "Ain't That a Shame," the tune co-written by Fats Domino and Dave Bartholomew that famously appeared on Cheap Trick'sAt Budokan.

Amusingly, Miller was already using the guitar Rick Nielsen had given him during Cheap Trick's acceptance speech: an axe featuring, appropriately, the Miller Beer logo. In a nod to his forebears, Miller played the guitar behind his head at one point during the jam.

Prior to the performance, while the bands were setting up, Nielsen played emcee and introduced many of the musicians on the stage. He also expressed regret that he didn't get a chance to do a song with N.W.A., who did not end up performing last night.

Chicago, who had been eligible since 1994, earlier claimed victory in fan voting. Deep Purple, whose absence has long been pegged as one of the hall's most egregious errors, first became eligible for induction – like Miller – in 1993. Cheap Trick has been eligible since 2002.

All four original members of the beloved Rockford band were inducted. This included drummer Bun E. Carlos, whose in-limbo status with the group prompted a court battle.

N.W.A. rounded out the list of honorees at tonight's 31st annual Rock and Roll Hall of Fame induction ceremony, held at Barclays Center in Brooklyn, N.Y. The event will be broadcast by HBO on April 30.